Question

explain the variation in acceleration due to gravity with height and depth​

Answer 1

$\mathfrak{ \huge{ \red{ \underline{ \underline{Answer}}}}}$

$\star \: \: \boxed{ \blue{variation \: in \: g \: due \: to \: depth}} \\ \\ \implies \: variation \: in \: g \: due \: to \: depth \: d \: follows \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \orange{g \propto \: d}} \\ \\ \implies \: \boxed{ \blue{g = g(1 - \frac{d}{r})}} \\ \\ \implies \: d = depth \: and \: r = radii \: of \: earth \\ \\ \star \: \: \boxed{ \blue{variation \: in \: g \: due \: to \: height}} \\ \\ \implies \: variation \: in \: g \: due \: to \: height \: h \: follows \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \orange{g \propto \: \frac{1}{ {r}^{2} }}} \\ \\ \implies \: \boxed{ \blue{g = \frac{g}{ ({1 + \frac{h}{r}) }^{2} }}} \\ \\ \implies \: h = height \: from \: surface \: of \: earth$